From DE 10 2011 051 481 A1 a bumper arrangement is known, in which, starting out from the back of a bumper cross member, two crash boxes extend in vehicle longitudinal direction in order to be compressed and absorb collision energy in the event of the vehicle colliding with an obstacle. Portions of the bumper cross member projecting over the cross boxes are supported and stiffened through support elements, each of which extends along an outside of the crash box adjacent to it obliquely to the longitudinal direction of said crash box. The support elements of this conventional arrangement substantially have the shape of plates, on which ribs extend for stiffening, and each of which have angled end pieces at a front or rear edge facing the bumper cross member or the crash box. The end pieces contact the bumper cross member or a side wall of the crash box and are fastened to these through bolts. When the support elements during a collision are loaded with a minor overlap, forces between them and the bumper cross member or the crash box can be substantially transmitted only via the bolts. Because of this, the force transmission is concentrated on small wall regions of the crash box, and a correspondingly high wall thickness is required in order to avoid tearing-out of the bolts and as a consequence rendering the support elements inactive. The support elements can substantially yield to loading only through buckling and yielding in lateral direction. However, as soon as a support element starts to buckle it can only put up minor resistance to deformation, so that the amount of energy which can be absorbed by the support element is small relative to the quantity of material employed.